PROCEEDINGS 
OF THE 
Cambridge J^ilosop|kal Jtodelj). 
“ Ignoration of coordinates'' as a problem in linear substitutions. 
By T. J. I’ A. Bromwich, M.A., St John’s College. 
[Received 24 April 1901.] 
The method known in dynamics by the name of “ ignoration 
of coordinates” has received a good deal of attention at the 
hands of writers on dynamics ; but it does not seem to have been 
examined at all from the point of view of linear substitutions. 
The object of the following is to explain how we are led to the 
usual results by simple examination of the linear equations from 
which we start. 
Suppose that we have (m+n) quantities f 2 , . .., rj n 
given as linear functions of (m 4- n ) others x 1} x 2 , x m , y 1} y 2 , ...,y n 
by the equations 
_13F _ 137 /r= 1, 2, ...» ra\ 
fr_ 2foT’ v ‘~2d y,’ U = l, 2, 
where V is a quadratic function of the x’s and y s. We are now 
going to express f x , . .., f m , y } , . y n in terms of^, rj 1} . . ., rjn] 
and to do so let the equations for the f’s and fs be written in 
the symbolical form 
% = Px + Qy, 
7} = Rx + Sy, 
where P, S are square matrices of m and n rows respectively, 
while Q is a rectangular matrix of m rows and n columns, and R 
is one of n rows and m columns. 
VOL. XI. PT. III. 13 
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